How do you do this problem?

The probability that the conveyor belt will function for a month with one breakdown is approximately 0.17, or 17%, when rounded to two decimal places.

To find the probability that the conveyor belt will function for a month with one breakdown given a Poisson distribution with λ = 2.8, we can use the following formula:

P(X = k) = (e^(-λ) * (λ^k)) / k!

Where:
- P(X = k) is the probability of having k breakdowns in a month
- e is the base of the natural logarithm (approximately 2.71828)
- λ is the average number of breakdowns per month (2.8)
- k is the desired number of breakdowns in a month (1)

Now, let's plug in the values and calculate the probability:

P(X = 1) = (e^(-2.8) * (2.8^1)) / 1!

P(X = 1) = (0.0608 * 2.8) / 1

P(X = 1) ≈ 0.1702

So, the probability that the conveyor belt will function for a month with one breakdown is approximately 0.17, or 17%, when rounded to two decimal places.

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The equation of the straight lines are:

For m = 6 and (x1, y1) = (2, 8)  => y = 6x - 4

For m = 7 and (x1, y1) = (2, 10) => y = 7x - 4

We know that the equation of a line with gradient m and y-intercept is:

y = mx + c.

We need to find the equation of each of the straight lines, given its gradient and the coordinates of a point on the line.

We know the point-slope form of equation of line,

(y - y1) = m(x - x1)

For m = 6 and (x1, y1) = (2, 8)

(y - 8) = 6(x - 2)

y - 8 = 6x - 12

y = 6x - 4

For m = 7 and (x1, y1) = (2, 10)

(y - 10) = 7(x - 2)

y - 10 = 7x - 14

y = 7x - 4

Therefore,  the equation of the straight lines are:

For m = 6 and (x1, y1) = (2, 8)  => y = 6x - 4

For m = 7 and (x1, y1) = (2, 10) => y = 7x - 4

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Constructing the four lines that intersect the circumference of the circle and form the square.

To construct a circle inscribed in a square, first draw a square with the desired side length.

Next, draw two diagonals from opposite corners of the square. This will divide the square into four quadrants. Measure the length of each diagonal.

Divide the length of each diagonal by two and mark the midpoints of each diagonal.

This will create four points which will define the circle. Connect each of the midpoints with a curved line to form a circle inscribed in the square.

Finally, use a compass to adjust the curve of the circle until it is perfectly symmetrical.

The circle should be perfectly centered in the square and tangent to each of its sides.

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Answer: (A) Set compass to the diameter of the circle.

Step-by-step explanation:

The possible volumes of plastic used for each hemisphere, to the nearest cubic millimeter, are approximately 381 cubic millimeters and 696 cubic millimeters.

To find the possible volumes of the plastic used for each hemisphere, we need to calculate the volume within the 10% error interval.

First, we need to find the minimum and maximum diameters within the error interval.

Given that the diameter is 1cm with a 10% error interval, we can calculate the minimum and maximum diameters as follows:

Minimum diameter = 1cm - (10% of 1cm) = 1cm - 0.1cm = 0.9cm
Maximum diameter = 1cm + (10% of 1cm) = 1cm + 0.1cm = 1.1cm

Next, we can calculate the minimum and maximum radii by dividing the diameters by 2:

Minimum radius = 0.9cm / 2 = 0.45cm
Maximum radius = 1.1cm / 2 = 0.55cm

Now, we can calculate the minimum and maximum volumes using the formula for the volume of a sphere:

Minimum volume = (4/3) * π * (0.45cm)^3 ≈ 0.381 cubic centimeters
Maximum volume = (4/3) * π * (0.55cm)^3 ≈ 0.696 cubic centimeters

To convert the volumes to cubic millimeters, we need to multiply by 1000 since there are 1000 cubic millimeters in a cubic centimeter:

Minimum volume = 0.381 * 1000 ≈ 381 cubic millimeters
Maximum volume = 0.696 * 1000 ≈ 696 cubic millimeters

Therefore, the possible volumes of plastic used for each hemisphere, to the nearest cubic millimeter, are approximately 381 cubic millimeters and 696 cubic millimeters.

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Approximately 204.11 years ago, your great, great, great, great grandmother left you $2 in a bank account that has grown to $150,000 today.

To calculate the number of years, we can use the compound interest formula:

\(A = P(1 + r/n)^ {nt}\)

where A is the final amount, P is the principal amount, r is the annual interest rate (as a decimal), n is the number of times the interest is compounded per year, and t is the number of years.

Given that the principal amount is $2, the final amount is $150,000, the annual interest rate is 5.5% (0.055 as a decimal), and the interest is compounded weekly (n = 52), we can solve for t:

\(50,000 = 2(1 + 0.055/52)^{52t}\)

Dividing both sides by $2 and isolating the exponent, we get:

\(75,000 = (1.0010576923076923)^{52t}\)

Taking the logarithm of both sides, we have:

\(log(75,000) = log(1.0010576923076923)^{52t}\)

Using logarithm properties, we can rewrite the equation as:

log(75,000) = 52t * log(1.0010576923076923)

Solving for t by dividing both sides by 52 * log(1.0010576923076923), we find:

t ≈ 204.11 years

Therefore, approximately 204.11 years ago, your great, great, great, great grandmother left you $2 in the bank account.

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Answer:

Refer to the attached image.

Step-by-step explanation:

The value of h in the expression A=1/2h(c+d) is h = 2A/(c+d)

The subject of an equation is the variable that is been solved for. When you've solved an equation for the subject, your subject is the variable by itself on either the left or right side of the equation.

for example, in the equation A=1/2h(c+d), A is the subject of formula. changing the subject to h, we have to evacuate all other terms associative with h

multiplying both sides by 2

2A= h(c+d)

dividing both sides by (c+d)

therefore h= 2A/(c+d)

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Problem 5

There are 2 answers and they are choice B and choice C

We can tell by looking at the factors. For something like choice B, the factor (x+6) shows up twice, so that means x = -6 is a double root. Something like choice A has roots x = -6 and x = 6 which aren't the same.

========================================

Problem 6

Ted is correct. He set each factor equal to 0 and solved each equation that resulted from doing so.

Note how 3x-2 = 0 turns into 3x = 2 after adding 2 to both sides. Then he divided both sides by 3 to get x = 2/3. That's the first solution. The second solution x = -5 results from solving x+5 = 0. You subtract 5 from both sides.

To fix Maggie's mistake, you just need to correct her steps to mirror Ted's steps.

Answer:

B

Step-by-step explanation:

This is a problem using the Pythagorean theorem.

The square of the length required is 122 + 122 + 302 = 1188

The length is the square root of this number; I will leave it to you to extract the square root.

Answer:

34.47

Step-by-step explanation:

The change in profit (ΔP) when the number of units (Δx) increases by 5, based on the given marginal profit function, is -18331.50

To find the change in profit (ΔP) when the number of units (Δx) increases by 5.

we need to evaluate the marginal profit function and multiply it by Δx.

The marginal profit function is given by dP/dx = 12.1(60 - 3x).

We are given the value of x as 121, so we can substitute it into the marginal profit function to find the marginal profit at that point.

dP/dx = 12.1(60 - 3(121))

= 12.1(60 - 363)

= 12.1(-303)

= -3666.3

Now, we can calculate the change in profit (ΔP) by multiplying the marginal profit by Δx, which is 5 in this case.

ΔP = dP/dx×Δx

= -3666.3 × 5

= -18331.5

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It will take 5 minutes to print a batch of newspapers if 20 printers are used.

What is proportionality?

Proportionality is a mathematical relationship between two variables, where one variable is a constant multiple of the other. In other words, two quantities are proportional if they maintain a constant ratio to each other, meaning that as one quantity increases or decreases, the other quantity changes in the same proportion.

We are given that the time it takes to print a batch of newspapers, m, is inversely proportional to the number of printers used, n, and the equation of proportionality is:

m = k/n

where k is a constant of proportionality. We are also given that when k = 100, the equation is satisfied. So we can substitute k = 100 into the equation to get:

m = 100/n

To find the time it will take to print a batch of newspapers if 20 printers are used, we can substitute n = 20 into the equation:

m = 100/20 = 5

So it will take 5 minutes to print a batch of newspapers if 20 printers are used. Rounded to 1 decimal place, the answer is 5.0 minutes.

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Answer:

1581.75 = 55.75p + 968.5

Step-by-step explanation:

subtract 968.5 from both sides

613.5 = 55.75p

divide both sides

11 = p

The number of players the team can bring to the tournament will be 11.

A linear equation is an equation that has the variable of the highest power of 1. The standard form of a linear equation is of the form Ax + B = 0.

It is given that the Members of a lacrosse team raised $1581.75 to go to a tournament. They all rented a bus for $968.50 and budgeted $55.75 per player for meals.

Then an equation that can be used to determine p, the number of players the team can bring to the tournament will be;

1581.75 = 55.75p + 968.5

Now subtract 968.5 from both sides;

613.5 = 55.75p

Then divide both sides;

11 = p

Therefore, the number of players the team can bring to the tournament will be 11.

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Answer:

10.23% to the nearest hundredth.

Step-by-step explanation:

This is a Binomial Probability Distribution.

If exactly 25 are left handed then exactly 5 are right handed.

So (probability that exactly 25 are left handed)

= 30C5*(0.1)^5(0.9)^25

= 0.1023047706

= 10.23%.

The probability that exactly 25 students out of 30 are left-handed, assuming the researchers' claim is true, is approximately 0.2031, or about 20.31%.

It is the chance of an event to occur from a total number of outcomes.

The formula for probability is given as:

Probability = Number of required events / Total number of outcomes.

Example:

The probability of getting a head in tossing a coin.

P(H) = 1/2

We have,

This problem involves the binomial probability distribution, where we have a fixed number of trials (30 students in this case), and each trial has two possible outcomes (left-handed or not left-handed).

The probability of success (a student being left-handed) is 0.9, based on the researchers' claim.

The probability of a failure (a student not being left-handed) is 1 - 0.9 = 0.1.

We want to find the probability that exactly 25 students out of 30 are left-handed.

This can be calculated using the binomial probability formula:

\(P(X = k) = ^nC_ kp^k (1 - p)^{n-k}\)

where:

n = 30 (the number of trials)

k = 25 (the number of successes we want)

p = 0.9 (the probability of success in each trial)

Plugging in the values, we get:

\(P(X = 25) = ^{30}C_ {25}~ 0.9^{25} ~0.1^5\)

Using a calculator or statistical software, we can find that:

P(X = 25) ≈ 0.2031

Therefore,

The probability that exactly 25 students out of 30 are left-handed, assuming the researchers' claim is true, is approximately 0.2031, or about 20.31%.

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Answer:

The fraction in simplest form is: 25/3

The final angular speed of the disc was found to be 7 rad/s.

Now, we are supposed to calculate the angular speed of the platform once the men have leapt off. This means we need to find the final angular speed (w’) of the disc after the men have leapt off. This problem can be solved using the law of conservation of angular momentum.

Conservation of Angular Momentum According to the law of conservation of angular momentum, the total angular momentum of a system remains constant when no external torque acts on it.

Mathematically, it can be expressed as:

L1 = L2

where L1 = initial angular momentum

L2 = final angular momentum

Initial Angular Momentum

Initial angular momentum (L1) is calculated as follows:

For the disc, L1 = Iω

Where I = moment of inertia

ω = angular velocity

ω = w + Ω (relative angular speed)

Ω = 0, as the disc is at rest

L1 = I (w)For the men,

\(L1 = ∑ L′i = ∑ m′i ri2ω′\)

Where m′i = reduced mass of ith manri = perpendicular distance from the axis, ω′ = angular speed of man relative to the platform, r = radius of the platform. Here, the platform has a uniform mass distribution, so the moment of inertia can be calculated as, I = (1/2) mr2L1 = (1/2)mr2(w) + ∑ m′i ri2ω′ ...(1)

Final Angular MomentumFinal angular momentum (L2) is calculated as:

L2 = I′ ω′′Where I′ = moment of inertia of the platform once the men have leapt off

ω′′ = final angular speed of the platform, I′ = (1/2) mr2 + ∑ m′i ri2

Using the conservation of angular momentum,

\(L1 = L2(1/2)mr2(w) + ∑ m′i ri2ω′ = (1/2)mr2 + ∑ m′i ri2ω′′ω′′ = {(1/2)mr2(w) + ∑ m′i ri2ω′}/ [(1/2)mr2 + ∑ m′i ri2]\)

Substituting the given values,

\(ω′′ = {(1/2) (16 × 80) (7)}/ [(1/2) (16 × 80)]= 7 rad/s\)

Therefore, the final angular speed of the disc is 7 rad/s.

The problem of a circular platform in the shape of a disc with 16 men on it and a uniform mass distribution was discussed in this problem. The men start jumping simultaneously with an angular speed of 7it/s relative to the platform, which is stationary. The problem was solved using the law of conservation of angular momentum.

According to this law, the total angular momentum of a system remains constant when there is no external torque acting on it. This law was applied in two stages, first for the initial angular momentum and then for the final angular momentum.

The law of conservation of angular momentum was used to calculate the final angular momentum of the disc. This law was expressed mathematically as L1 = L2, where L1 was the initial angular momentum of the disc and L2 was the final angular momentum of the disc. L1 was calculated using the moment of inertia and the angular speed of the disc when it was at rest. L2 was calculated using the moment of inertia and the final angular speed of the disc after the men had jumped off. The moment of inertia was calculated using the formula I = (1/2)mr2, where m is the mass of the platform and r is the radius of the platform.

The problem was solved using the law of conservation of angular momentum. The final angular speed of the disc was found to be 7 rad/s. This problem demonstrated the application of the law of conservation of angular momentum in solving problems related to rotating objects.

The final angular speed of the circular platform was calculated using the law of conservation of angular momentum. The problem involved a platform in the shape of a disc with 16 men on it and a uniform mass distribution. The men jumped off simultaneously with an angular speed of 7it/s relative to the platform. The law of conservation of angular momentum was applied in two stages to calculate the final angular momentum of the disc. The moment of inertia was calculated using the formula I = (1/2)mr2. The final angular speed of the disc was found to be 7 rad/s.

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Type of Attention Impact on Encoding Process

1. Sustained attention Facilitates thorough encoding of information.

2. Selective attention Enhances encoding of attended stimuli while filtering out irrelevant information.

3. Divided attention Impairs encoding by dividing attentional resources among multiple tasks.

4. Exogenous attention Captures attention involuntarily, potentially interrupting the encoding process.

5. Endogenous attention Voluntarily directed attention that can prioritize specific information for encoding.

1. Sustained attention: Sustained attention refers to the ability to maintain focus over an extended period. It has a positive impact on the encoding process as it allows for thorough and comprehensive encoding of information.

2. Selective attention: Selective attention involves focusing on specific stimuli while filtering out irrelevant information. It enhances the encoding process by directing attention to the relevant stimuli, promoting their effective encoding.

3. Divided attention: Divided attention refers to the attempt to allocate attention to multiple tasks simultaneously. Dividing attention among multiple tasks impairs the encoding process as attentional resources become fragmented, leading to less effective encoding of information.

4. Exogenous attention: Exogenous attention is captured involuntarily by external stimuli, potentially interrupting the encoding process. It can divert attention away from the intended encoding task, resulting in a negative impact on encoding.

5. Endogenous attention: Endogenous attention is voluntarily directed attention that allows individuals to prioritize specific information for encoding. It enhances the encoding process by selectively focusing on relevant stimuli and allocating cognitive resources accordingly.

Different types of attention have varying impacts on the encoding process. Sustained attention and selective attention positively influence encoding, while divided attention and exogenous attention have negative effects. Endogenous attention, on the other hand, can enhance encoding by prioritizing specific information.

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Answer:

9 and 11

Step-by-step explanation:

there is a difference of 2 between consecutive odd integers.

let n and n + 2 be the integers , then

n + n + 2 = 20

2n + 2 = 20 ( subtract 2 from both sides )

2n = 18 ( divide both sides by 2 )

n = 9

and n + 2 = 9 + 2 = 11

the two consecutive odd numbers are 9 and 11

Answer:

Step-by-step explanation:

The resultant of these two forces is 780.31N

If the car has a mass of 3200 kg, the acceleration of the car is 0.244m/s²

The formula for the resultant force is expressed as:

\(R =\sqrt{(\sum F_x)^2+(\sum F_y)^2}\)

Take the sum of force along the horizontal

\(\sum F_x = 450cos10^0+380cos30^0\\\sum F_x =443.16 + 329.09\\\sum F_x = 772.25N\)

Take the sum of force along the vertical

\(\sum F_y = 450sin10^0-380sin30^0\\\sum F_y=78.14 - 190\\\sum F_y= -111.86N\)

Get the resultant force:

\(R =\sqrt{(772.25)^2+(-111.86)^2}\\R = \sqrt{596,370.0625 +12,512.6596}\\R = \sqrt{608,882.7221}\\R = 780.31N\)

Hence the resultant of these two forces is 780.31N

b) According to Newton's second law of motion;

\(R =ma\\a=\frac{R}{m} \\a=\frac{780.31}{3200}\\a = 0.244m/s^2\)

Hence If the car has a mass of 3200 kg, the acceleration of the car is 0.244m/s²

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Answer:

Let h be the height of the triangle.

Set your calculator to degree mode.

\( \tan(71) = \frac{26}{h} \)

\(h \tan(71) = 26\)

\(h = \frac{26}{ \tan(71) } = 8.9525\)

So the area of this triangle is

(1/2)(26)(8.9525) = 116.3827 square feet

The length of the hypotenuse is

\( \ \sqrt{ {( \frac{26}{ \tan(71) } )}^{2} + {26}^{2} } \)

\( \sqrt{ {8.9525}^{2} + {26}^{2} } = 27.4981\)

So the perimeter of this triangle is

8.9525 + 26 + 27.4981 = 62.4506 feet

Interest groups facilitate citizen participation in governance by mobilizing people to take collective action through voting, fundraising, and informing the public and elected officials about their issues.

Higher Placement The College Board's Advanced Placement Program makes a college-level course and exam in United States Government and Politics available to high school students.

By organizing people to take collective action through voting, fundraising, and informing the public and elected officials about their issues, interest groups enable citizen participation in governance.

a group of individuals united by a shared interest or objective and working to sway public policy. group leaders. As adolescents gain knowledge, they frequently form their own groups. government.

Therefore, interest groups facilitate citizen participation in governance by mobilizing people to take collective action through voting, fundraising, and informing the public and elected officials about their issues.

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The number of cases per batch that should be produced to minimize cost is: 300 units

The number of cases per batch that should be produced to minimize cost can be found by using the Economic Order Quantity.

The Economic Order Quantity (EOQ) is a calculation performed by a business that represents the ideal order size that allows the business to meet demand without overspending. The inventory manager calculates her EOQ to minimize storage costs and excess inventory.  

Thus:

Number of cases per batch = √((2 * Setup costs * annual demand)/ holding costs for the year)

Solving gives:

√((2 * 30 * 15000)/10)

= √90000

= 300 units

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Answer:

Angle CEB

Step-by-step explanation:

They are vertical angles

:]

The largest area that can be enclose in straight wall is 2450 m².

Let 'x' be the length of rectangle.

Let 'y' be the width rectangle.

Perimeter =  140 meters

2x + y = 140      

y = 140 - 2x

Area = xy

Put the value of y in area.

Area = x(-2x + 140)

Area = -2x² + 140x

Differentiating the area with respect to x.

dA/dx = -4x + 140

Put dA/dx = 0 to get the critical point.

-4x + 140 = 0

x = 140/4

x = 35

Largest area at x = 35.

y = 140 - 2x

y = 140 - 2×35

y = 70

Area = xy

Area = 70×35

Area = 2450 m²

Thus, the largest area that can be enclose in straight wall is 2450 m².

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Answer:

a. x=1

b. x=18/5

Step-by-step explanation:

Answer:

200 - x = y ; when y is not student council and x is student council

or 200 - 157 = 43

Step-by-step explanation:

I. The only clues we got here are total students is 200, student council and not student counsin.

  - 85 kids of student council play sport.

  - 72 kids of student council not play sport.

So the total of student counsin is

   = 85 + 72

 x  = 157

II. Find the kids who are not student council

When total student - student council = not student council

           200 - x = y

           200 - 157 = 43

So  y  = 43

That makes 43 kids of students who aren't student council.

Hope that help :)

Answer:

2 units

Step-by-step explanation:

From one crest (high point) to the next crest  point is one period....

  this covers 2 units on this graph